Titu Andreescu, University of Texas at Dallas, and
Branislav Kisavcanin, NVIDIA Corporation, and AwesomeMath

Math Leads for Mathletes (Book 2)
Rich Resource for Young Math Enthusiasts, Parents, Teachers, and Mentors

A publication of XYZ Press.
ISBN: 978-0-9968745-5-7
Series, Volume: XYZ Series, Volume 30

Bibliographic Information:
Published: 15 April 2018; Copyright Year: 2018;
Pages: 230; Hardcover; List Price: US$54.95; Itemcode: XYZ/30
Subject Classification General Interest
Math Education

Readership:

Middle school students interested in mathematics competition preparation.

Description:

Math Leads for Mathletes Book 2 is part of the Math Leads for Mathletes series, providing
more challenging units for young math problem solvers and many others! The book
draws on the authorsf experience working with young mathletes and on the collective wisdom
of mathematics educators around the world to help parents and mentors challenge and teach
their aspiring math problem solvers. The topics contained in this book are best suited for
middle schoolers, although students who discovered competitive mathematics in later grades
will also benefit from the material. This book will help students advance in several directions
important in competitive mathematics: algebra, combinatorics, geometry, and number theory.
It presents a variety of problem solving strategies and challenges readers to explain their solutions,
write proofs, and explore connections with other problems.

Table of Contents

Eberhard Kaniuth, and Anthony To-Ming Lau,
University of Alberta, Edmonton, AB, Canada

Fourier and Fourier-Stieltjes Algebras on
Locally Compact Groups

ISBN: 978-0-8218-5365-8
Series, Volume: Mathematical Surveys and Monographs, Volume 231

Bibliographic Information: Published: 24 June 2018; Copyright Year: 2018;
Pages: 306; Hardcover; List Price: US$122; Itemcode: SURV/231
Subject Classification : Analysis
Supplementary Text

Readership:

Graduate students and researchers interested in abstract harmonic analysis, Banach
algebras, and operator spaces.

Description:

The theory of the Fourier algebra lies at the crossroads of several areas of analysis.
Its roots are in locally compact groups and group representations, but it requires a considerable
amount of functional analysis, mainly Banach algebras. In recent years it has made a major
connection to the subject of operator spaces, to the enrichment of both. In this book two
leading experts provide a road map to roughly 50 years of research detailing the role that the
Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the
nature of locally compact groups, but also in building bridges between abstract harmonic analysis,
Banach algebras, and operator algebras. All of the important topics have been included,
which makes this book a comprehensive survey of the field as it currently exists.
Since the book is, in part, aimed at graduate students, the authors offer complete and readable
proofs of all results. The book will be well received by the community in abstract harmonic
analysis and will be particularly useful for doctoral and postdoctoral mathematicians conducting
research in this important and vibrant area.

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Nitya Kitchloo, Mona Merling, Johns Hopkins University, Baltimore, MD,
Jack Morava, Johns Hopkins University,Baltimore, MD,
Emily Riehl, Johns Hopkins University, Baltimore, MD,
and W. Stephen Wilson, Johns Hopkins University, Baltimore, MD,

New Directions in Homotopy Theory

ISBN: 978-1-4704-3774-9
Series, Volume: Contemporary Mathematics, Volume 707:

Bibliographic Information: Published: 25 June 2018; Copyright Year: 2018;
Pages: approximately 197; Softcover; List Price: US$117;
Subject Classification Geometry and Topology

Readership:

Graduate students and research mathematicians interested in algebraic topology,
homotopy theory, and category theory.

Description:

This volume contains the proceedings of the Second Mid-Atlantic Topology
Conference, held from March 12?13, 2016, at Johns Hopkins University in Baltimore,
Maryland.

The focus of the conference, and subsequent papers, was on applications of innovative methods
from homotopy theory in category theory, algebraic geometry, and related areas,
emphasiz-ing the work of younger researchers in these fields.

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John M. Erdman, Portland State University, OR

A Problems Based Course in Advanced Calculus

ISBN: 978-1-4704-4246-0
Series, Volume: Pure and Applied Undergraduate Texts, Volume 32

Bibliographic Information:
Published: 20 July 2018; Copyright Year: 2018;
Pages: approximately 365; Hardcover; List Price: US$79;
Subject Classification : Logic and Foundations
Supplementary Text

Readership:

Undergraduate students interested in introduction to proofs.

Description:

This textbook is suitable for a course in advanced calculus that promotes active
learning through problem solving. It can be used as a base for a Moore method or inquiry
based class, or as a guide in a traditional classroom setting where lectures are organized
around the presentation of problems and solutions. This book is appropriate for any student
who has taken (or is concurrently taking) an introductory course in calculus. The book
includes sixteen appendices that review some indispensable prerequisites on techniques of
proof writing with special attention to the notation used the course.

Table of Contents

Theo Buhler, and Dietmar A. Salamon, ETH, Zurich, Switzerland

Functional Analysis

ISBN: 978-1-4704-4190-6
Series, Volume: Graduate Studies in Mathematics, Volume 191
Bibliographic Information: Published: 16 July 2018; Copyright Year: 2018;
Pages: approximately 472; Hardcover; List Price: US$83;
Subject Classification : Algebra and Algebraic Geometry
Supplementary Text

Readership:

Graduate students and researchers interested in teaching and learning functional analysis.

Description:

Functional analysis is a central subject of mathematics with applications in many areas of
geometry, analysis, and physics. This book provides a comprehensive introduction to the field for graduate
students and researchers.
It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzela?Ascoli theorem,
elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental
principles of functional analysis (uniform boundedness, open mapping theorem, Hahn?Banach theorem) and
discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes
the theorems of Banach?Alaoglu, Banach?Dieudonne, Eberlein??mulyan, Kre&ibreve;n?Milman, as well as an
introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm
theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed
image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex
Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand
spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators
and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and
spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to
strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual
semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a
discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes
the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem.
With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-twosemester
course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and
linear algebra, as well as some foundational material from the second-year courses on point set topology,
complex analysis in one variable, and measure and integration.

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